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The acceleration of fast deflagration waves. (English) Zbl 0564.76110

In an earlier paper the authors [Trans. 28th Conf. Army Math., Bethesda/Md. 1982, ARO Rep. 83-1 (1983; Zbl 0533.00003) on pp. 133-142] gave a theory of steady deflagration waves based on an ignition- temperature model obtained from Arrhenius kinetics. They were able to describe analytically the structure of deflagration waves for the entire range of wave speeds between zero and the maximum (Chapman-Jouget) value. In this paper we construct a quasi-steady theory of flame acceleration based on that work, which can predict the acceleration response of a preexisting flame to quite arbitrary hydrodynamic disturbances in the limit of small heat release during the combustion. Explicit formulas and criteria are developed. In particular we find that an unsteady deflagration wave can travel at speeds in excess of the Chapman-Jouget value, and even at arbitrarily large supersonic values.

MSC:

76V05 Reaction effects in flows
80A25 Combustion

Citations:

Zbl 0533.00003
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References:

[1] ; , Theory of Laminar Flames, Cambridge: University Press 1982, Ch. I. · Zbl 0557.76001 · doi:10.1017/CBO9780511569531
[2] ; , Nonlinear Waves, Ithaca, New York: Cornell University Press 1974, Ch. 4.
[3] Lu, SIAM J. Appl. Math. 42 pp 625– (1982)
[4] Stewart, Journal de Mecanique
[5] Stewart, Transactions of the 28th Conference of Army Mathematicians
[6] Stewart, Journal de Mécanique
[7] Combustion Theory. Reading, Massachusetts: Addison-Wesely Publishing Co. 1965, Ch. 2.
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